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Combining semidefinite and polyhedral relaxations for integer programs

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Integer Programming and Combinatorial Optimization (IPCO 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 920))


We present a general framework for designing semidefinite relaxations for constrained 0–1 quadratic programming and show how valid inequalities of the cut-polytope can be used to strengthen these relaxations. As examples we improve the ϑ-function and give a semidefinite relaxation for the quadratic knapsack problem. The practical value of this approach is supported by numerical experiments which make use of the recent development of efficient interior point codes for semidefinite programming.

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Egon Balas Jens Clausen

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© 1995 Springer-Verlag Berlin Heidelberg

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Helmberg, C., Poljak, S., Rendl, F., Wolkowicz, H. (1995). Combining semidefinite and polyhedral relaxations for integer programs. In: Balas, E., Clausen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1995. Lecture Notes in Computer Science, vol 920. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59408-6

  • Online ISBN: 978-3-540-49245-0

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